A propagator theory applied to wave mechanics in phase space

Abstract

The fact that the classical Liouville equation can be analyzed as a dynamical equation in Hilbert-Koopman (HK) space is used in order to develop a perturbative method for the wave mechanics in phase space: an explicit solution of the Liouville equation in qp representation is exhibited. The connection between the solution obtained and the dynamics of correlations is established by computing the qp-kp transformation function in HK space. To elucidate the method, an application is presented and the result compared to that available in the literature.